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| author | Kristian Evers <kristianevers@gmail.com> | 2018-04-30 22:42:59 +0200 |
|---|---|---|
| committer | Kristian Evers <kristianevers@gmail.com> | 2018-04-30 22:57:05 +0200 |
| commit | 970d708ff9d796f7d9ec00b22023e835fbdc7f2d (patch) | |
| tree | cbee11737ed36f20e51ba19c9e8faa757e79ac0d /docs/source/operations/projections | |
| parent | cd23e5f1b2630ee07567bd361373ba725774061b (diff) | |
| download | PROJ-970d708ff9d796f7d9ec00b22023e835fbdc7f2d.tar.gz PROJ-970d708ff9d796f7d9ec00b22023e835fbdc7f2d.zip | |
Refactor operation doc pages
Extended the use of the :option: directive to all currently written
operation doc pages. In the process several more default parameters were
added for easy inclusion in other doc pages.
Expanded the info tables for each operation with "domain", "alias",
"input type" and "output type".
Corrected various errors along the way. Mainly formatting errors and
references to invalid parameters such as +sym in hatano.
Diffstat (limited to 'docs/source/operations/projections')
24 files changed, 624 insertions, 166 deletions
diff --git a/docs/source/operations/projections/aea.rst b/docs/source/operations/projections/aea.rst index d4a4c1de..4fcd3cac 100644 --- a/docs/source/operations/projections/aea.rst +++ b/docs/source/operations/projections/aea.rst @@ -4,23 +4,42 @@ Albers Equal Area ******************************************************************************** +---------------------+----------------------------------------------------------+ -| **Classification** | Conic. | +| **Classification** | Conic | +---------------------+----------------------------------------------------------+ -| **Available forms** | Forward and inverse, spherical and elliptical projection.| +| **Available forms** | Forward and inverse, spherical and elliptical projection | +---------------------+----------------------------------------------------------+ -| **Defined area** | Global. | +| **Defined area** | Global | +---------------------+----------------------------------------------------------+ +| **Alias** | aea | +---------------------+----------------------------------------------------------+ -| **Options** | +| **Domain** | 2D | +---------------------+----------------------------------------------------------+ -| `+lat_1` | First standard parallel. Defaults to 0.0. | +| **Input type** | Geodetic coordinates | +---------------------+----------------------------------------------------------+ -| `+lat_2` | Second standard parallel. Can not be equal to `lat_1`. | -| | Defaults to 0.0. | +| **Output type** | Projected coordinates | +---------------------+----------------------------------------------------------+ + .. image:: ./images/aea.png :scale: 50% :alt: Albers Equal Area +Options +################################################################################ + +.. note:: All options are optional for the Albers Equal Area projection. + +.. include:: ../options/lat_1.rst + +.. include:: ../options/lat_2.rst + +.. include:: ../options/lon_0.rst + +.. include:: ../options/ellps.rst + +.. include:: ../options/R.rst + +.. include:: ../options/x_0.rst + +.. include:: ../options/y_0.rst diff --git a/docs/source/operations/projections/aeqd.rst b/docs/source/operations/projections/aeqd.rst index d4baa8b6..4663af3e 100644 --- a/docs/source/operations/projections/aeqd.rst +++ b/docs/source/operations/projections/aeqd.rst @@ -8,14 +8,13 @@ Azimuthal Equidistant +---------------------+----------------------------------------------------------+ | **Available forms** | Forward and inverse, spherical and elliptical projection | +---------------------+----------------------------------------------------------+ -| **Implemented by** | Gerald I. Evenden | +| **Alias** | aeqd | +---------------------+----------------------------------------------------------+ -| **Options** | +| **Domain** | 2D | +---------------------+----------------------------------------------------------+ -| `+guam` | Use Guam elliptical formulas. Only accurate near the | -| | Island of Guam (:math:`\lambda\approx 144.5^{\circ}`, | -| | :math:`\phi\approx 13.5^{\circ}`) | -| | Defaults to false. | +| **Input type** | Geodetic coordinates | ++---------------------+----------------------------------------------------------+ +| **Output type** | Projected coordinates | +---------------------+----------------------------------------------------------+ @@ -23,3 +22,29 @@ Azimuthal Equidistant :scale: 50% :alt: Azimuthal Equidistant + +Options +################################################################################ + +.. note:: All options are optional for the Azimuthal Equidistant projection. + +.. option:: +guam + + Use Guam elliptical formulas. Only accurate near the Island of Guam + (:math:`\lambda\approx 144.5^{\circ}`, :math:`\phi\approx 13.5^{\circ}`) + +.. include:: ../options/k_0.rst + +.. include:: ../options/lat_ts.rst + +.. include:: ../options/lat_0.rst + +.. include:: ../options/lon_0.rst + +.. include:: ../options/x_0.rst + +.. include:: ../options/y_0.rst + +.. include:: ../options/ellps.rst + +.. include:: ../options/R.rst diff --git a/docs/source/operations/projections/airy.rst b/docs/source/operations/projections/airy.rst index eefda4e9..1c856d0a 100644 --- a/docs/source/operations/projections/airy.rst +++ b/docs/source/operations/projections/airy.rst @@ -9,26 +9,47 @@ within the small or great circle defined by an angular distance, :math:`\phi_b`, from the tangency point of the plane :math:`( \lambda_0, \phi_0 )`. +---------------------+----------------------------------------------------------+ -| **Classification** | | +| **Classification** | Azimuthal | +---------------------+----------------------------------------------------------+ | **Available forms** | Forward spherical projection | +---------------------+----------------------------------------------------------+ | **Defined area** | Global | +---------------------+----------------------------------------------------------+ -| **Implemented by** | Gerald I. Evenden | +| **Alias** | airy | +---------------------+----------------------------------------------------------+ -| **Options** | ++ **Domain** | 2D | +---------------------+----------------------------------------------------------+ -| `+lat_b` | Angular distance from tangency point of the plane | -| | :math:`( \lambda_0, \phi_0 )` where the error is kept at | -| | minimum. Defaults to :math:`90^{\circ}` which is | -| | suitable for hemispherical maps. | +| **Input type** | Geodetic coordinates | +---------------------+----------------------------------------------------------+ -| `+no_cut` | Do not cut at hemisphere limit | +| **Output type** | Projected coordinates | +---------------------+----------------------------------------------------------+ + .. image:: ./images/airy.png :scale: 50% :alt: Airy +Options +################################################################################ + +.. option:: +lat_b + + Angular distance from tangency point of the plane :math:`( \lambda_0, \phi_0 )` + where the error is kept at minimum. + + *Defaults to 90° (suitable for hemispherical maps).* + +.. option:: +no_cut + + Do not cut at hemisphere limit + +.. include:: ../options/lat_0.rst + +.. include:: ../options/lon_0.rst + +.. include:: ../options/x_0.rst + +.. include:: ../options/y_0.rst + +.. include:: ../options/R.rst diff --git a/docs/source/operations/projections/aitoff.rst b/docs/source/operations/projections/aitoff.rst index 14b9177a..92ef2f12 100644 --- a/docs/source/operations/projections/aitoff.rst +++ b/docs/source/operations/projections/aitoff.rst @@ -10,9 +10,28 @@ Aitoff +---------------------+----------------------------------------------------------+ | **Defined area** | Global | +---------------------+----------------------------------------------------------+ - +| **Alias** | aitoff | ++---------------------+----------------------------------------------------------+ +| **Domain** | 2D | ++---------------------+----------------------------------------------------------+ +| **Input type** | Geodetic coordinates | ++---------------------+----------------------------------------------------------+ +| **Output type** | Projected coordinates | ++---------------------+----------------------------------------------------------+ .. image:: ./images/aitoff.png :scale: 50% :alt: Aitoff +Parameters +################################################################################ + +.. note:: All parameters for the projection are optional. + +.. include:: ../options/lon_0.rst + +.. include:: ../options/R.rst + +.. include:: ../options/x_0.rst + +.. include:: ../options/y_0.rst diff --git a/docs/source/operations/projections/alsk.rst b/docs/source/operations/projections/alsk.rst index 659de33b..d08fa827 100644 --- a/docs/source/operations/projections/alsk.rst +++ b/docs/source/operations/projections/alsk.rst @@ -1,7 +1,7 @@ .. _alsk: ******************************************************************************** -Mod. Stererographics of Alaska +Modified Stererographics of Alaska ******************************************************************************** +---------------------+----------------------------------------------------------+ | **Classification** | Modified azimuthal | @@ -10,8 +10,29 @@ Mod. Stererographics of Alaska +---------------------+----------------------------------------------------------+ | **Defined area** | Alaska | +---------------------+----------------------------------------------------------+ +| **Alsk** | alsk | ++---------------------+----------------------------------------------------------+ +| **Domain** | 2D | ++---------------------+----------------------------------------------------------+ +| **Input type** | Geodetic coordinates | ++---------------------+----------------------------------------------------------+ +| **Output type** | Projected coordinates | ++---------------------+----------------------------------------------------------+ + .. image:: ./images/alsk.png :scale: 50% :alt: Mod. Stererographics of Alaska +Options +################################################################################ + +.. note:: All options are optional for the projection. + +.. include:: ../options/x_0.rst + +.. include:: ../options/y_0.rst + +.. include:: ../options/ellps.rst + +.. include:: ../options/R.rst diff --git a/docs/source/operations/projections/apian.rst b/docs/source/operations/projections/apian.rst index 096adf44..6b5e247d 100644 --- a/docs/source/operations/projections/apian.rst +++ b/docs/source/operations/projections/apian.rst @@ -11,8 +11,31 @@ Apian Globular I +---------------------+----------------------------------------------------------+ | **Defined area** | Global | +---------------------+----------------------------------------------------------+ +| **Alias** | apian | ++---------------------+----------------------------------------------------------+ +| **Domain** | 2D | ++---------------------+----------------------------------------------------------+ +| **Input type** | Geodetic coordinates | ++---------------------+----------------------------------------------------------+ +| **Output type** | Projected coordinates | ++---------------------+----------------------------------------------------------+ + .. image:: ./images/apian.png :scale: 50% :alt: Apian Globular I +Options +################################################################################ + +.. note:: All options are optional for the Apian Globular projection. + +.. include:: ../options/lat_0.rst + +.. include:: ../options/lon_0.rst + +.. include:: ../options/R.rst + +.. include:: ../options/x_0.rst + +.. include:: ../options/y_0.rst diff --git a/docs/source/operations/projections/calcofi.rst b/docs/source/operations/projections/calcofi.rst index 4a29c812..8a240ebd 100644 --- a/docs/source/operations/projections/calcofi.rst +++ b/docs/source/operations/projections/calcofi.rst @@ -14,12 +14,15 @@ California Cooperative Oceanic Fisheries Investigations program, known as CalCOF +---------------------+----------------------------------------------------------+ | **Defined area** | Only valid for the west coast of USA and Mexico | +---------------------+----------------------------------------------------------+ -| **Implemented by** | Frank Warmerdam | +| **Alias** | calcofi | +---------------------+----------------------------------------------------------+ -| **Options** | +| **Domain** | 2D | +---------------------+----------------------------------------------------------+ -| `No special options for this projection` | +| **Input type** | Geodetic coordinates | +---------------------+----------------------------------------------------------+ +| **Output type** | Projected coordinates | ++---------------------+----------------------------------------------------------+ + .. image:: ../../../images/calcofi.png @@ -67,6 +70,15 @@ Output of the above command:: 80.0 60.0 -121.15 34.15 +Options +################################################################################ + +.. note:: All options are optional for the CalCOFI projection. + +.. include:: ../options/ellps.rst + +.. include:: ../options/R.rst + Mathematical definition ################################################################################ diff --git a/docs/source/operations/projections/cass.rst b/docs/source/operations/projections/cass.rst index 4111a2ee..dba6a7c4 100644 --- a/docs/source/operations/projections/cass.rst +++ b/docs/source/operations/projections/cass.rst @@ -13,12 +13,15 @@ Although the Cassini projection has been largely replaced by the Transverse Merc +---------------------+-------------------------------------------------------------------------+ | **Defined area** | Global, but best used near the central meridian with long, narrow areas | +---------------------+-------------------------------------------------------------------------+ -| **Implemented by** | Gerald I. Evenden | +| **Alias** | cass | +---------------------+-------------------------------------------------------------------------+ -| **Options** | +| **Domain** | 2D | +---------------------+-------------------------------------------------------------------------+ -| `+lat_0` | Latitude of origin (Default to 0) | +| **Input type** | Geodetic coordinates | +---------------------+-------------------------------------------------------------------------+ +| **Output type** | Projected coordinates | ++---------------------+-------------------------------------------------------------------------+ + .. image:: ./images/cass.png :scale: 50% @@ -42,6 +45,24 @@ Example using EPSG 3068 (Soldner Berlin):: $ echo 13.5 52.4 | proj +proj=cass +lat_0=52.41864827777778 +lon_0=13.62720366666667 +x_0=40000 +y_0=10000 +ellps=bessel +datum=potsdam +units=m +no_defs 31343.05 7932.76 +Options +################################################################################ + +.. note:: All options are optional for the Cassini projection. + +.. include:: ../options/lat_0.rst + +.. include:: ../options/lon_0.rst + +.. include:: ../options/x_0.rst + +.. include:: ../options/y_0.rst + +.. include:: ../options/ellps.rst + +.. include:: ../options/R.rst + + Mathematical definition ####################### diff --git a/docs/source/operations/projections/ccon.rst b/docs/source/operations/projections/ccon.rst index 8a858e38..f5ceed67 100644 --- a/docs/source/operations/projections/ccon.rst +++ b/docs/source/operations/projections/ccon.rst @@ -4,8 +4,10 @@ Central Conic ******************************************************************************** -This is central (centrographic) projection on cone tangent at ``lat_0`` latitude, -identical with ``conic()`` projection from ``mapproj`` R package. +.. versionadded:: 5.0.0 + +This is central (centrographic) projection on cone tangent at :option:``lat_1`` +latitude, identical with ``conic()`` projection from ``mapproj`` R package. +---------------------+----------------------------------------------------------+ | **Classification** | Conic | @@ -14,13 +16,16 @@ identical with ``conic()`` projection from ``mapproj`` R package. +---------------------+----------------------------------------------------------+ | **Defined area** | Global, but best used near the standard parallel | +---------------------+----------------------------------------------------------+ -| **Implemented by** | Lukasz Komsta | +| **Alias** | ccon | ++---------------------+----------------------------------------------------------+ +| **Domain** | 2D | +---------------------+----------------------------------------------------------+ -| **Options** | +| **Input type** | Geodetic coordinates | +---------------------+----------------------------------------------------------+ -| `+lat_1` | Latitude of standard parallel. | +| **Output type** | Projected coordinates | +---------------------+----------------------------------------------------------+ + .. image:: ./images/ccon.png :scale: 50% :alt: Central Conic @@ -44,13 +49,38 @@ The ATPOL coordinates can be achieved with with the following parameters: :: - +proj=ccon +lat_1=52 +lat_0=52 +lon_0=19 +axis=esu +a=6390000 +x_0=330000 +y_0=-350000 + +proj=ccon +lat_1=52 +lon_0=19 +axis=esu +a=6390000 +x_0=330000 +y_0=-350000 For more information see [Komsta2016]_ and [Verey2017]_. +Parameters +################################################################################ + +Required +------------------------------------------------------------------------------- + +.. option:: +lat_1=<value> + + Standard parallel of projection. + +Optional +------------------------------------------------------------------------------- + +.. include:: ../options/lon_0.rst + +.. include:: ../options/R.rst + +.. include:: ../options/x_0.rst + +.. include:: ../options/y_0.rst + + +Mathematical definition +################################################################################ + Forward projection -================== +------------------------------------------------------------------------------- .. math:: @@ -66,7 +96,7 @@ Forward projection Inverse projection -================== +------------------------------------------------------------------------------- .. math:: @@ -81,7 +111,7 @@ Inverse projection \lambda = \frac{\tan^{-1} \sqrt{x^2+y^2}}{\sin \phi_0} Reference values -================== +################################################################################ For ATPOL to WGS84 test, run the following script: diff --git a/docs/source/operations/projections/eqc.rst b/docs/source/operations/projections/eqc.rst index 5833bd61..de463034 100644 --- a/docs/source/operations/projections/eqc.rst +++ b/docs/source/operations/projections/eqc.rst @@ -13,15 +13,16 @@ The simplest of all projections. Standard parallels (0° when omitted) may be sp +---------------------+----------------------------------------------------------+ | **Defined area** | Global, but best used near the equator | +---------------------+----------------------------------------------------------+ -| **Implemented by** | Gerald I. Evenden | +| **Alias** | eqc | +---------------------+----------------------------------------------------------+ -| **Options** | +| **Domain** | 2D | +---------------------+----------------------------------------------------------+ -| `+lat_ts` | Latitude of true scale. Defaults to 0.0 | +| **Input type** | Geodetic coordinates | +---------------------+----------------------------------------------------------+ -| `+lat_0` | Center of the map : latitude of origin | +| **Output type** | Projected coordinates | +---------------------+----------------------------------------------------------+ + .. image:: ./images/eqc.png :scale: 50% :alt: Equidistant Cylindrical (Plate Carrée) @@ -67,6 +68,24 @@ Example using Plate Carrée projection with true scale at latitude 30° and cent $ echo -88 30 | proj +proj=eqc +lat_ts=30 +lon_0=90w 192811.01 3339584.72 +Parameters +################################################################################ + + +.. include:: ../options/lon_0.rst + +.. include:: ../options/lat_0.rst + +.. include:: ../options/lat_ts.rst + +.. include:: ../options/x_0.rst + +.. include:: ../options/y_0.rst + +.. include:: ../options/ellps.rst + +.. include:: ../options/R.rst + Mathematical definition ####################### diff --git a/docs/source/operations/projections/gall.rst b/docs/source/operations/projections/gall.rst index b9120d9f..bdb88895 100644 --- a/docs/source/operations/projections/gall.rst +++ b/docs/source/operations/projections/gall.rst @@ -7,22 +7,26 @@ Gall (Gall Stereographic) The Gall stereographic projection, presented by James Gall in 1855, is a cylindrical projection. It is neither equal-area nor conformal but instead tries to balance the distortion inherent in any projection. -+---------------------+--------------------------------------------------------------------------------+ -| **Classification** | Transverse and oblique cylindrical | -+---------------------+--------------------------------------------------------------------------------+ -| **Available forms** | Forward and inverse, Spherical | -+---------------------+--------------------------------------------------------------------------------+ -| **Defined area** | Global | -+---------------------+--------------------------------------------------------------------------------+ -| **Implemented by** | Gerald I. Evenden | -+---------------------+--------------------------------------------------------------------------------+ -| **Options** | No special options for this projection | -+---------------------+--------------------------------------------------------------------------------+ ++---------------------+----------------------------------------------------------+ +| **Classification** | Transverse and oblique cylindrical | ++---------------------+----------------------------------------------------------+ +| **Available forms** | Forward and inverse, Spherical | ++---------------------+----------------------------------------------------------+ +| **Defined area** | Global | ++---------------------+----------------------------------------------------------+ +| **Alias** | gall | ++---------------------+----------------------------------------------------------+ +| **Domain** | 2D | ++---------------------+----------------------------------------------------------+ +| **Input type** | Geodetic coordinates | ++---------------------+----------------------------------------------------------+ +| **Output type** | Projected coordinates | ++---------------------+----------------------------------------------------------+ .. image:: ./images/gall.png :scale: 50% - :alt: Gall (Gall Stereographic) + :alt: Gall (Gall Stereographic) Usage ##### @@ -38,7 +42,7 @@ Unlike the Mercator, the Gall shows the poles as lines running across the top an Example using Gall Stereographical :: - $ echo 9 51 | proj +proj=gall +lon_0=0 +x_0=0 +y_0=0 +ellps=WGS84 +datum=WGS84 +units=m +no_defs + $ echo 9 51 | proj +proj=gall +lon_0=0 +x_0=0 +y_0=0 +ellps=WGS84 +datum=WGS84 +units=m +no_defs 708432.90 5193386.36 Example using Gall Stereographical (Central meridian 90°W) :: @@ -46,6 +50,22 @@ Example using Gall Stereographical (Central meridian 90°W) :: $ echo 9 51 | proj +proj=gall +lon_0=90w +x_0=0 +y_0=0 +ellps=WGS84 +datum=WGS84 +units=m +no_defs 7792761.91 5193386.36 +Parameters +################################################################################ + +.. note:: All parameters for the projection are optional. + +.. include:: ../options/lon_0.rst + +.. include:: ../options/R.rst + +.. include:: ../options/x_0.rst + +.. include:: ../options/y_0.rst + +.. include:: ../options/ellps.rst + + Mathematical definition ####################### @@ -70,7 +90,7 @@ Inverse projection .. math:: - \phi = 2 \arctan( \frac{y}{1+\frac{\sqrt{2}}{2}} ) + \phi = 2 \arctan( \frac{y}{1+\frac{\sqrt{2}}{2}} ) .. math:: diff --git a/docs/source/operations/projections/geos.rst b/docs/source/operations/projections/geos.rst index cd576283..3dc914b3 100644 --- a/docs/source/operations/projections/geos.rst +++ b/docs/source/operations/projections/geos.rst @@ -3,6 +3,10 @@ ******************************************************************************** Geostationary Satellite View ******************************************************************************** + +The geos projection pictures how a geostationary satellite scans the earth at regular +scanning angle intervals. + +---------------------+----------------------------------------------------------+ | **Classification** | Azimuthal | +---------------------+----------------------------------------------------------+ @@ -10,16 +14,13 @@ Geostationary Satellite View +---------------------+----------------------------------------------------------+ | **Defined area** | Global | +---------------------+----------------------------------------------------------+ -| **Implemented by** | Gerald I. Evenden and Martin Raspaud | +| **Alias** | geos | +---------------------+----------------------------------------------------------+ -| **Options** | +| **Domain** | 2D | +---------------------+----------------------------------------------------------+ -| `+h` | Satellite height above earth. Required. | +| **Input type** | Geodetic coordinates | +---------------------+----------------------------------------------------------+ -| `+sweep` | Sweep angle axis of the viewing instrument. | -| | Valid options are ``x`` and ``y``. Defaults to ``y``. | -+---------------------+----------------------------------------------------------+ -| `+lon_0` | Subsatellite longitude point. | +| **Output type** | Projected coordinates | +---------------------+----------------------------------------------------------+ @@ -27,9 +28,6 @@ Geostationary Satellite View :scale: 50% :alt: Geostationary Satellite View -The geos projection pictures how a geostationary satellite scans the earth at regular -scanning angle intervals. - Usage ############################################################################### @@ -70,3 +68,33 @@ The sweep argument is used to tell PROJ which on which axis the outer-gimbal is rotating. The possible values are x or y, y being the default. Thus, the scanning geometry of the Meteosat series satellite should take sweep as x, and GOES should take sweep as y. + +Parameters +################################################################################ + +Required +------------------------------------------------------------------------------- + +.. include:: ../options/h.rst + + +Optional +------------------------------------------------------------------------------- + +.. option:: +sweep=<axis> + + Sweep angle axis of the viewing instrument. Valid options are *"x"* and *"y*". + + *Defaults to "y".* + +.. include:: ../options/lon_0.rst + +.. include:: ../options/R.rst + +.. include:: ../options/ellps.rst + +.. include:: ../options/x_0.rst + +.. include:: ../options/y_0.rst + + diff --git a/docs/source/operations/projections/hatano.rst b/docs/source/operations/projections/hatano.rst index 5d0c63b7..99e9ac3d 100644 --- a/docs/source/operations/projections/hatano.rst +++ b/docs/source/operations/projections/hatano.rst @@ -12,25 +12,37 @@ Hatano Asymmetrical Equal Area +---------------------+----------------------------------------------------------+ | **Available forms** | Forward and inverse, spherical projection | +---------------------+----------------------------------------------------------+ -| **Defined area** | Global, but best between standard parallels | +| **Defined area** | Global | +---------------------+----------------------------------------------------------+ -| **Implemented by** | Gerald I. Evenden | +| **Alias** | hatano | +---------------------+----------------------------------------------------------+ -| **Options** | +| **Domain** | 2D | +---------------------+----------------------------------------------------------+ -| `+lat_1` | Standard Parallel 1 | +| **Input type** | Geodetic coordinates | +---------------------+----------------------------------------------------------+ -| `+lat_2` | Standard Parallel 2 | -+---------------------+----------------------------------------------------------+ -| `+sym` | Symmetric form used instead of asymmetric | +| **Output type** | Projected coordinates | +---------------------+----------------------------------------------------------+ + .. image:: ./images/hatano.png :scale: 50% :alt: Hatano Asymmetrical Equal Area +Parameters +################################################################################ + +.. note:: All parameters for the projection are optional. + +.. include:: ../options/lon_0.rst + +.. include:: ../options/R.rst + +.. include:: ../options/x_0.rst + +.. include:: ../options/y_0.rst + Mathematical Definition -------------------------------------------------------------------------------- @@ -52,10 +64,10 @@ Forward ==================================== ================== =================== -Condition :math:`C_p` :math:`C_p` +Condition :math:`C_y` :math:`C_p` ==================================== ================== =================== -if ``+sym`` or :math:`\phi > 0` 1.75859 2.67595 -if not ``+sym`` and :math:`\phi < 0` 1.93052 2.43763 +For :math:`\phi > 0` 1.75859 2.67595 +For :math:`\phi < 0` 1.93052 2.43763 ==================================== ================== =================== For :math:`\phi = 0`, :math:`y \leftarrow 0`, and :math:`x \leftarrow 0.85\lambda`. diff --git a/docs/source/operations/projections/healpix.rst b/docs/source/operations/projections/healpix.rst index d05b2123..e13c5456 100644 --- a/docs/source/operations/projections/healpix.rst +++ b/docs/source/operations/projections/healpix.rst @@ -4,18 +4,21 @@ HEALPix ******************************************************************************** +---------------------+----------------------------------------------------------+ -| **Classification** | Mixed | +| **Classification** | Miscellaneous | +---------------------+----------------------------------------------------------+ | **Available forms** | Forward and inverse, spherical and elliptical projection | +---------------------+----------------------------------------------------------+ | **Defined area** | Global | +---------------------+----------------------------------------------------------+ -| **Implemented by** | Alex Raichev and Michael Speth | +| **Alias** | healpix | +---------------------+----------------------------------------------------------+ -| **Options** | +| **Domain** | 2D | +---------------------+----------------------------------------------------------+ -| `No special options for this projection` | +| **Input type** | Geodetic coordinates | +---------------------+----------------------------------------------------------+ +| **Output type** | Projected coordinates | ++---------------------+----------------------------------------------------------+ + .. image:: ../../../images/healpix.png :scale: 75% @@ -43,13 +46,23 @@ To run a forward HEALPix projection on a unit sphere model, use the following co # output 0 0 0.00 0.00 -Further reading +Parameters ################################################################################ -#. `NASA <http://healpix.jpl.nasa.gov/>`_ -#. `Wikipedia <https://en.wikipedia.org/wiki/HEALPix>`_ +.. note:: All parameters for the projection are optional. + +.. include:: ../options/lon_0.rst +.. include:: ../options/x_0.rst +.. include:: ../options/y_0.rst +.. include:: ../options/ellps.rst +.. include:: ../options/R.rst +Further reading +################################################################################ + +#. `NASA <http://healpix.jpl.nasa.gov/>`_ +#. `Wikipedia <https://en.wikipedia.org/wiki/HEALPix>`_ diff --git a/docs/source/operations/projections/merc.rst b/docs/source/operations/projections/merc.rst index 31ca250a..888b12a3 100644 --- a/docs/source/operations/projections/merc.rst +++ b/docs/source/operations/projections/merc.rst @@ -16,6 +16,8 @@ The projection is conformal which makes it suitable for navigational purposes. +---------------------+----------------------------------------------------------+ | **Defined area** | Global, but best used near the equator | +---------------------+----------------------------------------------------------+ +| **Alias** | merc | ++---------------------+----------------------------------------------------------+ + **Domain** | 2D | +---------------------+----------------------------------------------------------+ | **Input type** | Geodetic coordinates | @@ -52,16 +54,14 @@ Example using scaling factor:: Note that :option:`+lat_ts` and :option:`+k_0` are mutually exclusive. If used together, :option:`+lat_ts` takes precedence over :option:`+k_0`. -Options -######### - -.. note:: All options are optional for the Mercator projection. +Parameters +################################################################################ -.. include:: ../options/k_0.rst +.. note:: All parameters for the projection are optional. .. include:: ../options/lat_ts.rst -.. include:: ../options/lat_0.rst +.. include:: ../options/k_0.rst .. include:: ../options/lon_0.rst @@ -71,6 +71,8 @@ Options .. include:: ../options/ellps.rst +.. include:: ../options/R.rst + Mathematical definition ####################### diff --git a/docs/source/operations/projections/mill.rst b/docs/source/operations/projections/mill.rst index eb9c2092..718d4b9b 100644 --- a/docs/source/operations/projections/mill.rst +++ b/docs/source/operations/projections/mill.rst @@ -7,19 +7,22 @@ Miller Cylindrical The Miller cylindrical projection is a modified Mercator projection, proposed by Osborn Maitland Miller in 1942. The latitude is scaled by a factor of :math:`\frac{4}{5}`, projected according to Mercator, and then the result is multiplied by :math:`\frac{5}{4}` to retain scale along the equator. -+---------------------+--------------------------------------------------------------------------------+ -| **Classification** | Neither conformal nor equal area cylindrical | -+---------------------+--------------------------------------------------------------------------------+ -| **Available forms** | Forward and inverse spherical | -+---------------------+--------------------------------------------------------------------------------+ -| **Defined area** | Global, but best used near the equator | -+---------------------+--------------------------------------------------------------------------------+ -| **Implemented by** | Gerald I. Evenden | -+---------------------+--------------------------------------------------------------------------------+ -| **Options** | -+---------------------+--------------------------------------------------------------------------------+ -| `+lat_0` | Latitude of origin (Default to 0) | -+---------------------+--------------------------------------------------------------------------------+ ++---------------------+----------------------------------------------------------+ +| **Classification** | Neither conformal nor equal area cylindrical | ++---------------------+----------------------------------------------------------+ +| **Available forms** | Forward and inverse spherical | ++---------------------+----------------------------------------------------------+ +| **Defined area** | Global, but best used near the equator | ++---------------------+----------------------------------------------------------+ +| **Alias** | mill | ++---------------------+----------------------------------------------------------+ +| **Domain** | 2D | ++---------------------+----------------------------------------------------------+ +| **Input type** | Geodetic coordinates | ++---------------------+----------------------------------------------------------+ +| **Output type** | Projected coordinates | ++---------------------+----------------------------------------------------------+ + .. image:: ./images/mill.png :scale: 50% @@ -36,6 +39,19 @@ Example using Central meridian 90°W:: $ echo -100 35 | proj +proj=mill +lon_0=90w -1113194.91 4061217.24 +Parameters +################################################################################ + +.. note:: All parameters for the projection are optional. + +.. include:: ../options/lon_0.rst + +.. include:: ../options/R.rst + +.. include:: ../options/x_0.rst + +.. include:: ../options/y_0.rst + Mathematical definition ####################### diff --git a/docs/source/operations/projections/natearth.rst b/docs/source/operations/projections/natearth.rst index 57dd96db..4d304fab 100644 --- a/docs/source/operations/projections/natearth.rst +++ b/docs/source/operations/projections/natearth.rst @@ -10,12 +10,16 @@ Natural Earth +---------------------+--------------------------------------------------------+ | **Defined area** | Global | +---------------------+--------------------------------------------------------+ -| **Implemented by** | Bernhard Jenny | +| **Alias** | natearth | +---------------------+--------------------------------------------------------+ -| **Options** | +| **Domain** | 2D | +---------------------+--------------------------------------------------------+ -| `No special options for this projection` | +| **Input type** | Geodetic coordinates | +---------------------+--------------------------------------------------------+ +| **Output type** | Projected coordinates | ++---------------------+--------------------------------------------------------+ + + .. image:: ./images/natearth.png :scale: 50% @@ -40,6 +44,18 @@ an example of an inverse projection on a sphere with a radius of 7500 m:: $ echo 3500 -8000 | proj -I +proj=natearth +a=7500 37d54'6.091"E 61d23'4.582"S +Parameters +################################################################################ + +.. note:: All parameters for the projection are optional. + +.. include:: ../options/lon_0.rst + +.. include:: ../options/R.rst + +.. include:: ../options/x_0.rst + +.. include:: ../options/y_0.rst Further reading ################################################################################ diff --git a/docs/source/operations/projections/nsper.rst b/docs/source/operations/projections/nsper.rst index d204305b..d7611587 100644 --- a/docs/source/operations/projections/nsper.rst +++ b/docs/source/operations/projections/nsper.rst @@ -7,25 +7,42 @@ Near-sided perspective The near-sided perspective projection simulates a view from a height :math:`h` similar to how a satellite in orbit would see it. -+---------------------+-------------------------------------------------------------+ -| **Classification** | Azimuthal. Neither conformal nor equal area. | -+---------------------+-------------------------------------------------------------+ -| **Available forms** | Forward and inverse spherical projection | -+---------------------+-------------------------------------------------------------+ -| **Defined area** | Global, although for one hemisphere at a time. | -+---------------------+-------------------------------------------------------------+ -| **Options** | -+---------------------+-------------------------------------------------------------+ -| `+h` | Height of the view point above the Earth and must be in | -| | the same units as the radius of the sphere. Required. | -+---------------------+-------------------------------------------------------------+ -| `+lat_0` | Latitude (in degrees) of the view position. Defaults to 0. | -+---------------------+-------------------------------------------------------------+ -| `+lon_0` | Longitude (in degrees) of the view position. Defaults to 0. | -+---------------------+-------------------------------------------------------------+ ++---------------------+----------------------------------------------------------+ +| **Classification** | Azimuthal. Neither conformal nor equal area. | ++---------------------+----------------------------------------------------------+ +| **Available forms** | Forward and inverse spherical projection | ++---------------------+----------------------------------------------------------+ +| **Defined area** | Global, although for one hemisphere at a time. | ++---------------------+----------------------------------------------------------+ +| **Alias** | nsper | ++---------------------+----------------------------------------------------------+ +| **Domain** | 2D | ++---------------------+----------------------------------------------------------+ +| **Input type** | Geodetic coordinates | ++---------------------+----------------------------------------------------------+ +| **Output type** | Projected coordinates | ++---------------------+----------------------------------------------------------+ .. image:: ./images/nsper.png :scale: 50% :alt: Near-sided perspective +Parameters +################################################################################ + +Required +------------------------------------------------------------------------------- + +.. include:: ../options/h.rst + +Optional +------------------------------------------------------------------------------- + +.. include:: ../options/lon_0.rst + +.. include:: ../options/R.rst + +.. include:: ../options/x_0.rst + +.. include:: ../options/y_0.rst diff --git a/docs/source/operations/projections/ortho.rst b/docs/source/operations/projections/ortho.rst index 1a8da63a..5e96e2a2 100644 --- a/docs/source/operations/projections/ortho.rst +++ b/docs/source/operations/projections/ortho.rst @@ -15,14 +15,30 @@ around a given latitude and longitude. | **Defined area** | Global, although only one hemisphere can be seen at a | | | time | +---------------------+--------------------------------------------------------+ -| **Options** | +| **Alias** | ortho | +---------------------+--------------------------------------------------------+ -| `+lon_0` | Longitudinal projection center. Defaults to 0.0. | +| **Domain** | 2D | +---------------------+--------------------------------------------------------+ -| `+lat_0` | Latitudinal projection center. Defaults to 0.0. | +| **Input type** | Geodetic coordinates | ++---------------------+--------------------------------------------------------+ +| **Output type** | Projected coordinates | +---------------------+--------------------------------------------------------+ .. image:: ./images/ortho.png :scale: 50% :alt: Orthographic +Parameters +################################################################################ + +.. note:: All parameters for the projection are optional. + +.. include:: ../options/lon_0.rst + +.. include:: ../options/lat_0.rst + +.. include:: ../options/R.rst + +.. include:: ../options/x_0.rst + +.. include:: ../options/y_0.rst diff --git a/docs/source/operations/projections/qsc.rst b/docs/source/operations/projections/qsc.rst index 740901e8..56d4ea3f 100644 --- a/docs/source/operations/projections/qsc.rst +++ b/docs/source/operations/projections/qsc.rst @@ -11,15 +11,16 @@ Quadrilateralized Spherical Cube +---------------------+----------------------------------------------------------+ | **Defined area** | Global | +---------------------+----------------------------------------------------------+ -| **Implemented by** | Martin Lambers | +| **Alias** | qsc | +---------------------+----------------------------------------------------------+ -| **Options** | +| **Domain** | 2D | +---------------------+----------------------------------------------------------+ -| `+lat_0` | Latitude (in degrees) of the view position. | +| **Input type** | Geodetic coordinates | +---------------------+----------------------------------------------------------+ -| `+lon_0` | Longitude (in degrees) of the view position. | +| **Output type** | Projected coordinates | +---------------------+----------------------------------------------------------+ + The purpose of the Quadrilateralized Spherical Cube (QSC) projection is to project a sphere surface onto the six sides of a cube: @@ -151,6 +152,21 @@ The resulting images can be laid out in a grid like below. | | |bottomside| | | | +------------+--------------+-------------+------------+ +Parameters +################################################################################ + +.. note:: All parameters for the projection are optional. + +.. include:: ../options/lon_0.rst + +.. include:: ../options/lat_0.rst + +.. include:: ../options/ellps.rst + +.. include:: ../options/x_0.rst + +.. include:: ../options/y_0.rst + Further reading ################################################################################ diff --git a/docs/source/operations/projections/rhealpix.rst b/docs/source/operations/projections/rhealpix.rst index 52a913a5..caca5c7b 100644 --- a/docs/source/operations/projections/rhealpix.rst +++ b/docs/source/operations/projections/rhealpix.rst @@ -4,23 +4,22 @@ rHEALPix ******************************************************************************** +---------------------+----------------------------------------------------------+ -| **Classification** | Mixed | +| **Classification** | Miscellaneous | +---------------------+----------------------------------------------------------+ | **Available forms** | Forward and inverse, spherical and elliptical projection | +---------------------+----------------------------------------------------------+ | **Defined area** | Global | +---------------------+----------------------------------------------------------+ -| **Implemented by** | Alex Raichev and Michael Speth | +| **Alias** | rhealpix | +---------------------+----------------------------------------------------------+ -| **Options** | +| **Domain** | 2D | +---------------------+----------------------------------------------------------+ -| `+north_square` | Position of the north polar square. | -| | Valid inputs are 0--3. Defaults to 0. | +| **Input type** | Geodetic coordinates | +---------------------+----------------------------------------------------------+ -| `+south_square` | Position of the south polar square. | -| | Valid inputs are 0--3. Defaults to 0. | +| **Output type** | Projected coordinates | +---------------------+----------------------------------------------------------+ + .. image:: ../../../images/rhealpix.png :scale: 75% :alt: rHEALPix @@ -43,6 +42,31 @@ command:: > EOF 55 12 6115727.86 1553840.13 +Parameters +################################################################################ + +.. note:: All parameters for the projection are optional. + +.. option:: +north_square + + Position of the north polar square. Valid inputs are 0--3. + + *Defaults to 0.0.* + +.. option:: +south_square + + Position of the south polar square. Valid inputs are 0--3. + + *Defaults to 0.0.* + + +.. include:: ../options/lon_0.rst + +.. include:: ../options/ellps.rst + +.. include:: ../options/x_0.rst + +.. include:: ../options/y_0.rst Further reading ################################################################################ diff --git a/docs/source/operations/projections/tmerc.rst b/docs/source/operations/projections/tmerc.rst index 1fc0cd7e..cd864d13 100644 --- a/docs/source/operations/projections/tmerc.rst +++ b/docs/source/operations/projections/tmerc.rst @@ -6,21 +6,23 @@ Transverse Mercator The transverse Mercator projection in its various forms is the most widely used projected coordinate system for world topographical and offshore mapping. -+---------------------+--------------------------------------------------------------------------------+ -| **Classification** | Transverse and oblique cylindrical | -+---------------------+--------------------------------------------------------------------------------+ -| **Available forms** | Forward and inverse, Spherical and Elliptical | -+---------------------+--------------------------------------------------------------------------------+ -| **Defined area** | Global, but reasonably accurate only within 15 degrees of the central meridian | -+---------------------+--------------------------------------------------------------------------------+ -| **Implemented by** | Gerald I. Evenden | -+---------------------+--------------------------------------------------------------------------------+ -| **Options** | -+---------------------+--------------------------------------------------------------------------------+ -| `+lat_0` | Latitude of origin (Default to 0) | -+---------------------+--------------------------------------------------------------------------------+ -| `+k0` | Scale factor at natural origin (Default to 1) | -+---------------------+--------------------------------------------------------------------------------+ ++---------------------+----------------------------------------------------------+ +| **Classification** | Transverse and oblique cylindrical | ++---------------------+----------------------------------------------------------+ +| **Available forms** | Forward and inverse, Spherical and Elliptical | ++---------------------+----------------------------------------------------------+ +| **Defined area** | Global, but reasonably accurate only within 15 degrees | +| | of the central meridian | ++---------------------+----------------------------------------------------------+ +| **Alias** | tmerc | ++---------------------+----------------------------------------------------------+ +| **Domain** | 2D | ++---------------------+----------------------------------------------------------+ +| **Input type** | Geodetic coordinates | ++---------------------+----------------------------------------------------------+ +| **Output type** | Projected coordinates | ++---------------------+----------------------------------------------------------+ + .. image:: ./images/tmerc.png @@ -65,6 +67,25 @@ Example using Gauss Boaga on Italy area (EPSG:3004) :: $ echo 15 42 | proj +proj=tmerc +lat_0=0 +lon_0=15 +k=0.9996 +x_0=2520000 +y_0=0 +ellps=intl +units=m +no_defs 2520000.00 4649858.60 +Parameters +################################################################################ + +.. note:: All parameters for the projection are optional. + +.. include:: ../options/lon_0.rst + +.. include:: ../options/lat_0.rst + +.. include:: ../options/ellps.rst + +.. include:: ../options/R.rst + +.. include:: ../options/k_0.rst + +.. include:: ../options/x_0.rst + +.. include:: ../options/y_0.rst + Mathematical definition ####################### diff --git a/docs/source/operations/projections/tpers.rst b/docs/source/operations/projections/tpers.rst index 13d49cd7..1d36b07c 100644 --- a/docs/source/operations/projections/tpers.rst +++ b/docs/source/operations/projections/tpers.rst @@ -10,22 +10,17 @@ Tilted perspective +---------------------+----------------------------------------------------------+ | **Defined area** | Global | +---------------------+----------------------------------------------------------+ -| **Implemented by** | Gerald I. Evenden | +| **Alias** | tpers | +---------------------+----------------------------------------------------------+ -| **Options** | +| **Domain** | 2D | +---------------------+----------------------------------------------------------+ -| `+h` | Height (in meters) above the surface. Required. | +| **Input type** | Geodetic coordinates | +---------------------+----------------------------------------------------------+ -| `+azi` | Bearing (in degrees) from due north. | -+---------------------+----------------------------------------------------------+ -| `+tilt` | Angle (in degrees) away from nadir. | -+---------------------+----------------------------------------------------------+ -| `+lat_0` | Latitude (in degrees) of the view position. | -+---------------------+----------------------------------------------------------+ -| `+lon_0` | Longitude (in degrees) of the view position. | +| **Output type** | Projected coordinates | +---------------------+----------------------------------------------------------+ + .. image:: ./images/tpers.png :scale: 50% :alt: Tilted perspective @@ -34,6 +29,40 @@ Tilted perspective Tilted Perspective is similar to :ref:`nsper` (``nsper``) in that it simulates a perspective view from a height. Where ``nsper`` projects onto a plane tangent to the surface, Tilted Perspective orients the plane towards the direction of the -view. Thus, extra parameters azi and tilt are required beyond `nsper``'s ``h``. -As with ``nsper``, ``lat_0`` & ``lon_0`` are also required -for satellite position. +view. Thus, extra parameters specifying azimuth and tilt are required beyond +`nsper``'s ``h``. As with ``nsper``, ``lat_0`` & ``lon_0`` are +also required for satellite position. + +Parameters +################################################################################ + +Required +------------------------------------------------------------------------------- + +.. include:: ../options/h.rst + +Optional +------------------------------------------------------------------------------- + +.. option:: +azi=<value> + + Bearing in degrees away from north. + + *Defaults to 0.0.* + +.. option:: +tilt=<value> + + Angle in degrees away from nadir. + + *Defaults to 0.0.* + +.. include:: ../options/lon_0.rst + +.. include:: ../options/lat_0.rst + +.. include:: ../options/R.rst + +.. include:: ../options/x_0.rst + +.. include:: ../options/y_0.rst + diff --git a/docs/source/operations/projections/webmerc.rst b/docs/source/operations/projections/webmerc.rst index 0c465afc..92da2d45 100644 --- a/docs/source/operations/projections/webmerc.rst +++ b/docs/source/operations/projections/webmerc.rst @@ -4,6 +4,8 @@ Web Mercator / Pseudo Mercator ******************************************************************************** +.. versionadded:: 5.1.0 + The Web Mercator / Pseudo Mercator projection is a cylindrical map projection. This is a variant of the regular :ref:`merc` projection, except that the computation is done on a sphere, using the semi-major axis of the ellipsoid. @@ -22,14 +24,19 @@ From `Wikipedia <https://en.wikipedia.org/wiki/Web_Mercator>`_: +---------------------+----------------------------------------------------------+ | **Classification** | Cylindrical (non conformant if used with ellipsoid) | +---------------------+----------------------------------------------------------+ -| **Version** | Added in proj 5.1.0 | -+---------------------+----------------------------------------------------------+ | **Available forms** | Forward and inverse, spherical projection | +---------------------+----------------------------------------------------------+ | **Defined area** | Global, but best used near the equator | +---------------------+----------------------------------------------------------+ -| **Options** | Neither lat_0, lon_0, lat_ts or k_0 should be used. | +| **Alias** | webmerc | ++---------------------+----------------------------------------------------------+ +| **Domain** | 2D | +---------------------+----------------------------------------------------------+ +| **Input type** | Geodetic coordinates | ++---------------------+----------------------------------------------------------+ +| **Output type** | Projected coordinates | ++---------------------+----------------------------------------------------------+ + Usage ######## @@ -39,6 +46,17 @@ Example:: $ echo 2 49 | proj +proj=webmerc +datum=WGS84 222638.98 6274861.39 +Parameters +################################################################################ + +.. note:: All parameters for the projection are optional. + +.. include:: ../options/R.rst + +.. include:: ../options/x_0.rst + +.. include:: ../options/y_0.rst + Mathematical definition ####################### |